Influence of benzothiophene acceptor moieties on the non-linear optical properties of pyreno-based chromophores: first-principles DFT framework

Herein, a series of heterocyclic organic compounds (PYFD1–PYFD7) are designed with different acceptor moieties at the terminal position of a reference compound (PYFR) for nonlinear optical (NLO) active materials. The optoelectronic characteristics of the designed chromophores were investigated using density functional theory (DFT) calculations with the M06/6-311G(d,p) functional. Frontier molecular orbital (FMO) analysis revealed a significant decrease in the energy of the band gaps (2.340–2.602 eV) for the derivatives as compared to the PYFR reference compound (3.12 eV). An efficient transfer of charge from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) was seen, which was further corroborated by the density of states (DOS) and transition density matrix (TDM) heat maps. The results of the global reactivity parameters (GRPs) indicated that all derivatives exhibited greater softness (σ = 0.384–0.427 eV) and lower hardness (η = 0.394–1.302 eV) as compared to PYFR, indicating a higher level of polarizability in the derivatives. Moreover, all of the derivatives showed significant findings in terms of nonlinear optical (NLO) results as compared to the reference chromophore. PYFD2 showed the most effective NLO response (α = 1.861 × 10−22 and βtot = 2.376 × 10−28 esu), including a lowered band gap of 2.340 eV, the maximum softness value of 0.4273 eV, and the lowest hardness value of 1.170 eV as compared to other chromophores. The incorporation of different acceptors and thiophene as a π-spacer in this structural alteration significantly contributed to achieving remarkable NLO responses. Therefore, our findings may motivate experimentalists to synthesize these designed NLO active materials for the current advanced technological applications.


Introduction
Since the invention of laser light, the remarkable eld of nonlinear optics has attracted considerable attention owing to their capability to modify the frequency of incident light.Second-order NLO processes are used to apply the NLO effects in a variety of technological domains such as photonic devices, 1 optical switching, and optical communication. 2 In recent years, signicant efforts have been made in both theoretical and practical endeavors in the advancement of NLO materials. 3,4ome instances of NLO devices include frequency converters used in biological imaging technologies and soliton devices, which are used in the massive networked communications. 5,6 molecule needs to be stable in at least two states in which it can exhibit very different NLO responses 7 in order to achieve a signicant switching effect.Many scientists have spent years seeking efficient NLO materials including molecular dyes, polymer systems, articial and synthetic nanoparticles, and inorganic and organic semiconductor diodes. 8,9Organic NLO materials possess lower dielectric constant values, higher photoelectrical coefficients, lower development costs, and simpler reaction chemistry.Moreover, their greater ease of use, contribution to frameworks having electron delocalization and greater design freedom make them more favorable than inorganic NLO materials. 10,11Centric compounds have a greater capacity for the transfer of charge because donor and acceptor moieties are matched up with organic chromophores that are not based on fullerenes. 12Fullerene-free compounds are more exible in terms of their chemical structure, energy level, electron affinity, and synthesis.
In recent years, a signicant number of metal-free organic donor-acceptor complexes have been shown to be exceptional NLO compounds.These complexes exhibit strong intramolecular charge transfer (ICT) properties. 13One way that electrons can transport charge inside an electric eld is by the movement of electron clouds from the donor to acceptor segments through p-linkers.The ICT development creates a new D-p-A system by generating a "push-pull" interaction between the electron-donating and withdrawing groups.The push-pull congurations can effectively increase the NLO response, which in turn affects their charge separation, band gap, asymmetrical distribution of electrons and the absorption spectra. 14Therefore, by using a variety of donors, p-spacers or acceptor moieties, lower band gaps with larger rst hyperpolarizability values can be attained for D-p-A systems. 15everal systems with an effective push-pull architecture have been published in the literature, which include; D-A, D-p-A, A-D-A, D-A-p-A, D-D-A congurations. 16n the present study, we designed a novel family of D-p-A congured, strong push-pull chromophores (PYFD1-PYFD7) by using PYFR (ref.17) as the reference compound.These compounds are designed by replacing the benzene of PYFR with a highly conjugated system, i.e., 2-(7-phenyl-4aH-uoren-2-yl) thiophene (MFT), and then introducing a variety of electron-decient end-capped acceptor units (FDM, MOM, DTD, DID, ODM, DDM, DOM).According to the literature review, no such study has been reported that describes the NLO properties of PYFR and derived compounds (PYFD1-PYFD7).This report presents the results of an NLO study conducted on the designed D-p-A compounds.To address this research gap, the optoelectronic properties of these newly designed compounds are calculated by utilizing the density functional theory (DFT) and time-dependent DFT (TD-DFT) approach.These chromophores are expected to play a pivotal role in the NLO eld.It is believed that this work will inspire the development of metal-free organic molecules with extraordinary NLO capabilities.

Methodology
Quantum chemical studies of the p-conjugated systems (PYFR and its derivatives, i.e., PYFD1-PYFD7) were accomplished using the Gaussian 09 package. 18For this purpose, the DFT/ TDDFT approaches were utilized at the M06/6-311G(d,p) level. 19,20It was found that the above-mentioned level is the highly parameterized approximate new hybrid meta exchangecorrelation energy functional of density functional theory (DFT).][23][24] Therefore, we are interested in selecting the M06/6-311G(d,p) level for this study.Firstly, the molecular geometries were optimized to obtain their true minima structures at the ground state (S 0 ) for the aforesaid level of theory.All of the input les were viewed using the Gauss View 6.0 soware. 25The timedependent DFT approach was used to obtain their energy gaps (FMOs and DOS), chemical reactivity (GRPs), and exciton states (TDMs), whereas the hyper-conjugative interactions (NBOs) and non-linear optical (NLO) insights for the said molecules were calculated using the above-mentioned level of DFT.Natural bond orbitals (NBOs) analysis was also carried out.The total dipole moment (m total ), average linear polarizability (hai), 26 and rst (b tot ) 27 and second hyper-polarizabilities (g tot ) 28 were determined using the following eqn (1)- (4).
for SHG values and for EOPE values.

Results and discussion
The current effort focuses on the computational analysis of the NLO response of the designed organic compounds. 35Minor changes to the reference molecule (PYFR) led to the design of a series of derivatives (PYFD1-PYFD7), as shown in Fig. 1.Firstly, the p-spacer group of the reference compound is modied by the introduction of 2-methyl-5-(7-(p-tolyl)-4aH-uoren-2-yl) thiophene (MFT), which is now considered as the p-linker moiety in the designed chromophores.Further modi-cations in the derived compounds are made by replacing the previous acceptor group with more efficient acceptor groups, such as 36,37 As a result, seven derivatives (PYFD1-PYFD7) are developed with the modied structural moieties.The optimized structures of PYFR and PYFD1-PYFD7 are displayed in Fig. 2. In this study, the inuence of the elongated p-spacer and strongly electron-withdrawing acceptor moieties on the NLO responses, such as the average linear polarizability hai, and rst (b tot ) and second hyperpolarizabilities (g tot ), are investigated.Moreover, several other parameters, such as energy band gaps (E gap ), absorption spectra (UV-Vis), exciton dissociations (E b ), stabilization energies (NBOs) and global reactivity parameters (GRPs): the global soness (s), global electrophilicity index (u), global hardness (h), electronegativity (X), chemical potential (m), electron affinity (EA) and ionization potential (IP), are also investigated for the designed organic molecules.Cartesian coordinates of the reference and designed compounds are presented in Tables S1-S8 † This research study will make a signicant contribution to the eld of nonlinear optics (NLO) and will inspire other researchers in this eld.

Frontier molecular orbitals (FMOs) analysis
The frontier molecular orbitals (FMOs) theory is considered as a fundamental analysis in predicting the quantum chemical properties of any molecule. 38With the help of FMOs, physicists and chemists can describe various aspects of the studied molecules, including their UV-vis spectra, optical properties, electronic features, charge transfer, reactivity and molecular interactions.LUMO stands for the lowest unoccupied molecular orbital and it has a tendency to accept an electron, while HOMO stands for the highest occupied molecular orbital and it has the capacity to donate an electron. 39The HOMO-LUMO energy gap (DE) also provides key evidence related to ICT and NLO behavior. 40,41The compounds with high DE are chemically hard compounds with greater kinetic stability and lower chemical reactivity.In contrast, molecules with a lower E gap are soer, more reactive and less stable. 42The major ndings are shown in Table 1.Meanwhile, energy differences corresponding to HOMO-1/LUMO+1 and HOMO-2/LUMO+2 of the investigated compounds (PYFR and PYFD1-PYFD7) are illustrated in Table S9, † and their corresponding orbitals are shown in Fig. S1.† The computed HOMO/LUMO energies of PYFR are −5.455 and −2.164 eV, respectively, with the energy gap of 3.291 eV, as shown in Table 1.The E HOMO values were calculated as −5.715, −5.576, −5.577, −5.577, −5.573, −5.580 and −5.580 eV, while the E LUMO values were found to be −2.164,−3.641, −3.958, −3.992, −3.939, −3.869, −3.788 and −3.753 eV for PYFD1-PYFD7, respectively.Furthermore, their corresponding E gap values were observed as 3.291, 2.074, 1.618, 1.585, 1.638, 1.704, 1.792 and 1.827 eV, respectively.The derivatives exhibited smaller bandgaps than PYFR due to the introduction of various extended acceptors and the addition of the electronic p-bridge (2-methyl-5-(7-phenyl-4aH-uoren-2-yl)thiophene), which results in resonance and the promotion of the transfer of electron density in the D-p-A congured compounds.
All derivatives include strong electron-accepting substituents in their structures; hence, they all exhibit smaller E gap values than PYFR, which lie in the range of 2.074-1.585eV.PYFD2 shows the shortest E gap (1.618 eV) compared to all other chromophores due to the presence of a nitro (-NO 2 ) group, which has a strong electron-withdrawing property and may drive the electron density away from nearby atoms in a molecule.On the other hand, PYFD1 exhibits the largest band gap (2.074 eV), owing to the presence of the 2-(5-uoro-2-methylene-2,3-dihydro-1-H-inden-1-ylidene)malononitrile acceptor moiety (FDM).Due to the existence of the sulphonic acid (-SO 3 H) group, PYFD3 has shown a smaller band gap than PYFD2 (1.585 < 1.618 eV).Furthermore, in the PYFD4 molecule, the -SO 3 H group is replaced with a -CN group; hence, it depicted a higher band gap of 1.638 eV.In contrast to PYFD5 (1.704 eV), which contains the triuoromethyl groups (-CF 3 ) on its terminal acceptor, PYFD6 and PYFD7 possess -Cl and -F groups linked to their respective benzene rings, and showed enhanced energy gaps as 1.792 and 1.827 eV, respectively.In general, the energy gap trend is summarized as follows: Owing to the addition of the highly electron-withdrawing -NO 2 group in the acceptor moiety along with the modied p-linker in PYFD2, the rate of intramolecular charge transfer (ICT) is primarily enhanced, which has led to a decreased band gap as compared to all other derivatives.The molecular orbital energies and their band gaps calculated via DFT approach are a little bit higher than that of TD-DFT (Table S41 †).
Fig. 3 illustrates the counter surface diagrams of the FMOs, depicting the electron density distribution over different areas of the molecules.The reference compound (PYFR) displays a unique electronic distribution pattern, with its LUMO entirely covered with the electronic clouds.Conversely, in its HOMO, the electronic clouds are predominantly concentrated in the donor region and the p-spacer.For derivatives (PYFD1-PYFD7), the HOMOs exhibit electron density on their donor regions and partially over the p-spacer.Whereas, in their LUMOs, the acceptor part displays prominent electronic clouds and negligibly over the p-spacer region.

Global reactivity parameters (GRPs)
The energy gap (E LUMO -E HOMO ) is the primary determinant for assessing the global reactivity parameters (GRPs) via the application of Koopmans' theorem.GRPs include the global soness (s), global electrophilicity index (u), global hardness (h), electronegativity (X), chemical potential (m), electron affinity (EA) and ionization potential (IP), 43,44 which are determined by using eqn ( 8)- (15), and the calculated values are presented in Table 2.
The energy needed to remove an electron from the highest occupied molecular orbital (HOMO) is equal to the ionization potential (IP), which is used to determine the electron-donating and electron-accepting capabilities of an atom. 45In our studied compounds (PYFR and PYFD1-PYFD7), the ionization potential (IP) values existed within the range of 5.729-5.740eV.A similar parameter is known as electron affinity (EA), which denotes the electron accepting tendency of chromophores.The statistical values obtained for our designed molecules (PYFD1-PYFD7) are higher than the reference compound (PYFR), which is due to their higher tendency to receive electrons owing to the presence of strong acceptor groups.The decreasing order of EA of the studied compounds in eV is as follows: Electronegativity (X) is a chemical property which quanties the attraction of an atom towards the electrons in a chemical bond.The chemical potential (m) of a species facilitates comprehension of a compound's stability and reactivity.These metrics quantify the electrophilic strength of a compound.Moreover, there is a direct relationship of the chemical stability with the energy gap, chemical potential and global hardness of an organic compound, while they are inversely related to the reactivity and soness of a compound.Therefore, the soer molecules have a smaller bandgap, which makes them more reactive.The polarizability of molecules may be linked with their soness, since soer molecules are oen more polarized.Among all the designed compounds, PYFD2 showed the highest value of soness (s), i.e., 0.4273 eV −1 , which demonstrated the highest polarizability and increased reactivity.The extent of soness (s) was decreased to 0.4257 eV −1 in PYFD3.A decrease in the value is seen in the case of PYFD4, PYFD5, PYFD6 and PYFD7, with values at 0.4187, 0.4081, 0.3982 and 0.3944 eV −1 , respectively.The lowest s value, indicating minimal reactivity and lower polarizability, was found to be in PYFD1 as 0.3840 eV −1 .The observed order of global soness (s) is as follows: Similarly, in the case of its counter parameter, which is known as the global hardness (h), out of all the compounds, PYFR exhibited the highest value (2.006 eV), while PYFD7 was found to have the lowest value at 0.394 eV.
It is worth noting that all the chromophores exhibited greater global soness (0.3840-0.4273 eV −1 ) and lower hardness values (0.394-1.302 eV).The elevated levels of soness observed suggest the enhanced reactive nature of the investigated compounds.Overall, this study revealed that the molecules' exhibited efficient CT ability between their HOMOs and LUMOs leads to better polarizability and remarkable NLO behavior. 46

Density of states (DOS)
Density of states (DOS) plots play a crucial role in examining the distribution and positioning of HOMO and LUMO densities. 16hese plots are employed to investigate the correlation between chemical bonding and the overlap population of molecules with various acceptor-donor combinations. 47The present DOS study is conducted for PYFR and PYFD1-PYFD7 and the resulting graphical plots are displayed in Fig. 4.These visualizations offer detailed insight into the energy levels of the frontier orbitals and the electronic states within the molecules.Such information is fundamental for predicting the electronic and optical properties of the studied molecules.In conducting DOS investigations, the compounds under study are broken down into donor, p-core and end-capped acceptor units, each denoted by a distinct color (donor in red, p-spacer in green and acceptor in blue lines) in PYFD1-PYFD7.The alteration in the pattern of the charge distribution is inuenced by changes in the acceptor moieties, and is substantiated by the HOMO-LUMO percentages of DOS displayed in Table S10.† The data shown in the table depicts the percentages for all possible fragments of our studied chromophores.In the case of the reference molecule (PYFR), the donor shows a high percentage on the HOMO (83.4%), while there is 61.3% on the LUMO.Contrary to this, its p-spacer shows a greater contribution towards the LUMO as 38.7% and less contribution towards the HOMO (16.6%).Moreover, the acceptor moiety is absent in PYFR.For PYFD1-PYFD7, the maximum charge on HOMOs is located over the donor moieties, i.e., 83.1, 83.7, 83.8, 83.6, 83.5, 83.2 and 83.3%, correspondingly.While, in the case of LUMOs, the highest DOS percentages are recorded for acceptors such as 92.1, 80.8, 91.1, 91.6, 90.7, 91.6 and 92.3% in PYFD1-PYFD7, correspondingly.The p-spacer functions as a facilitator with intermediate charge contributions for HOMOs and LUMOs.However, slightly greater contributions of p-spacers are recorded for their HOMOs as 16.9, 16.2, 16.1, 16.3, 16.5, 16.8 and 16.6% for PYFD1-PYFD7, respectively.The positive region on the DOS graphs indicates the LUMOs peaks and the negative regions displayed corresponding peaks for HOMOs.The energy gap between HOMOs and LUMOs of the respective compounds can be marked via the distance between their foremost HOMO/ LUMO peaks from the graph.It can be depicted feasibly from the DOS plot that in the LUMO region, the blue peaks are highest, which supports the high acceptor participation in the LUMOs from Table S11.† Similarly, the HOMOs region showed dominant donor peaks (red colored).
The DOS analysis of our concerned molecules rmly supports their frontier orbitals studies.Moreover, it reveals the efficient delocalization of the electronic charge from the electron-rich donor towards the electron-decient acceptor, which is consistent in all of the designed compounds.

Natural bond orbitals (NBOs) analysis
NBOs analysis provides a comprehensive understanding of the intra-and intermolecular interactions between the donor and acceptor components, as well as insights into the conjugative interactions and charge transfer within the molecules. 48The stabilization energy E (2) associated with the donor-acceptor interactions can be effectively determined using the secondorder perturbation theory.In NBOs analysis, the donor (i) transfers the charge density to the acceptor (j) via the p-linker, facilitating the transfer of electronic charges. 49The delocalization of charges and the corresponding stabilization energies (E (2) ) of our investigated molecules (PYFR and PYFD1-PYFD7) can be calculated using eqn (16).The donor orbital occupancy (q i ), off-diagonal elements (3 i and 3 j ), and diagonal NBO Fock matrix elements (F i.j ) are used to calculate the stabilization energy (E (2) ) and can be expressed as follows: A higher E (2) indicates a more pronounced interaction between the electron donors, signifying increased conjugation through the entire system.Utilizing the same DFT functional, the NBOs analysis for the designed molecules is conducted, and the essential transitions are summarized in Table 3. ESI † regarding the interactions can be found in Tables S11 through S18, † providing additional details on the analysis.
Generally, the possible electronic transitions are as follows: s / s*, p / p*, LP / s* and LP / p*.Among above mentioned transitions, p / p* transitions are considered to be predominant, which occur due to the p-conjugation system, s / s* are weaker due to sigma bonds, and LP / s* and LP / p* are minutely prominent excitations.According to Table 1   The above-mentioned results showed that PYFD1 exhibited the extra stability (25.50 kcal mol −1 ) among the studied compounds.This is due to its prolonged hyper-conjugative interactions.Overall, the NBOs study revealed that the investigated chromophores are stabilized due to hyper-conjugation, which plays a key role in their better NLO responses.

Transition density matrix (TDM)
The transition density matrix (TDM) is a valuable tool used for determining the electronic charge transfer in the designed compounds (PYFD1-PYFD7) and the reference molecule (PYFR).The TDM is used to assess the correlation between the donor and acceptor parts in the excited state, as well as the localization and delocalization of electron-hole pairs. 50It is oen used to comprehensively analyze the magnitude and characteristics of transitions in the compounds under investigation. 51This study excludes the impact of the hydrogen atom since it makes a negligible contribution to electronic transitions.The TDM ndings for all of the developed compounds are shown in Fig. 5.In order to comprehend the transfer of charge density, we subdivided our reference compound (PYFR) into two components: a donor and a p-linker.The fabricated chromophores (PYFD1-PYFD7) are divided into three segments, namely D, p-linker, and A. The TDM maps exhibited a very efficient diagonal charge transfer (CT) coherence in all of the chromophores.In PYFR, the majority of the charge density is concentrated in the donor region.However, for all of the designed compounds, the majority of the electron density is located on the acceptor region.Only a small portion of the electron density is observed in the p-linker, as indicated by the green spots.These green spots demonstrate the successful transfer of electron coherence from the donor to the p-linker, which effectively facilitates the movement of electron density towards the acceptor without any trapping.The results from the TDM heat maps suggested that there is a well-dened and enhanced separation of excitons in the excited state, which is crucial for the advancement of the NLO material.

Binding energy (E b )
The binding energy is a crucial and promising factor for determining the optoelectronic characteristics.It aids in identifying the possibility for excitation dissociation.Decreasing the binding energy reduces the strength of the coulombic interactions between the hole and electron, resulting in improved exciton dissociation in the excited state. 52It is determined by subtracting the HOMO-LUMO energy gap from the rst exciton energy.The binding energy (E b ) values of the PYFR and PYFD1-PYFD7 compounds were determined using eqn (17).
The symbol E b represents the binding energy, E L-H indicates the bandgap and E opt denotes the initial excitation energy.The calculated results for the binding energy are shown in Table 4.
The data presented above indicate that all of the chromophores had lower binding energy values (0.365 to 0.571 eV) compared to the reference chromophore (0.670 eV).This reduced E b can be attributed to the alteration in their structure, resulting in a robust push-pull conguration.The lower excitation and band gap energy levels result in a decreased binding energy, which in turn facilitates greater excitation dissociation and higher charge mobility rate.This leads to superior optoelectronic characteristics.The binding energy values decrease in the following order: PYFR > PYFD3 > PYFD4 > PYFD2 > PYFD5 > PYFD7 > PYFD6 > PYFD1.Molecules with low binding energy values have a strong correlation with polarizability.From previous studies, it was observed that the molecules with E b values below 1.9 eV are regarded as excellent photonic materials, which exhibit a notable NLO response.Notably, all of our derivatives exhibited a binding energy below 1.9 eV, indicating their potential as NLO materials due to their substantial charge separation in excited states.

UV-vis analysis
The UV-Vis spectroscopic technique was conducted to elucidate the absorption spectra related to the excited states in PYFR and PYFD1-PYFD7.This analysis provided insights into the probability of charge transfer, congurations driving these transitions and the inherent nature of electronic transitions in these systems.Table 5 shows the calculations for the maximum absorption wavelengths (l max ), excitation energies (E), oscillation strengths (f os ) and contributions from the molecular orbitals for the studied compounds.However, a detailed analysis is shown in Tables S19-S34.† Fig. 6 depicts the UV-Vis absorption spectra of the designed compounds, revealing the absorbance peaks in the gas and solvent mediums.
In chloroform solvent, the PYFD2 compound exhibits the highest absorption wavelength at 583.592 nm, which is attributed to its potent electron-withdrawing nitro groups in the acceptor unit, along with the lowest transition energy value of 2.125 eV.The corresponding oscillation strength of 0.059 can be observed with 89% HOMO to LUMO contribution.The presence of the lowest electron-withdrawing acceptor group in PYFD1 might result in the minimum l max , specically a hypochromic shi with a value of 528.807 nm.This shi is accompanied by the highest excitation energy of 2.345 eV.To enhance the maximum absorption wavelength (l max ) in the designed compounds, electron-withdrawing acceptor moieties are utilized.The presence of effective electron-withdrawing endcapped acceptors in the compounds leads to a red-shi in the absorption spectrum, causing a change in the absorption maxima (l max ) towards longer wavelengths.PYFD4 has a slightly longer absorption wavelength at 572.147 nm and a higher transition energy of 2.167 eV as compared to PYFD2.This change can be attributed to the addition of electronwithdrawing cyano groups.PYFD5 exhibits a higher absorption wavelength at 557.408 nm as compared to PYFD6.This difference is attributed to the replacement of triuoromethyl groups with chlorine, potentially resulting in a relatively longer wavelength in the UV region in PYFD5.The lower l max value (541.345nm) with high transition energy (2.290 eV) observed in PYFD7 as compared to PYFD6 could potentially be attributed to the removal of the chlorine group as it entrapped the charges and the substitution of uoro groups at the terminal acceptor.This electron-withdrawing effect reduces resonance, resulting in a higher band gap.The descending order of l max values in nm is as follows: PYFD2 (583.592)> PYFD3 (582.195)> PYFD4 (572.147)> PYFD5 (557.408)> PYFD6 (544.818)> PYFD7 (541.345)> PYFD1 (528.807)> PYFR (372.347).
The calculated l max values for the designed derivatives consistently exhibited higher values when measured in the gas phase as compared to chloroform.The l max values calculated in the gaseous phase for all the studied compounds fall within the range of 553-697 nm, which is higher than the l max value recorded for PYFR (371.032nm).Among the reference and designed compounds, PYFD3 displayed the most signicant absorption peak at 697.363 nm and the lowest excitation energy of 1.778 eV.This can be ascribed to the introduction of sulphonic acid (-SO 3 H) groups into the acceptor moiety.Their presence leads to a higher absorption peak due to its strong electron-withdrawing nature, enhancing the charge transfer interactions and inuencing electronic transitions.The following decreasing order is obtained in nm in the gaseous phase: PYFD3 (697.363)> PYFD2 (685.981)> PYFD4 (671.419)> PYFD5 (629.777)> PYFD6 (591.923)> PYFD7 (589.082)> PYFD1 (553.649)> PYFR (371.032).
Overall, a red-shi is depicted in the designed D-p-A organic molecules as compared to the reference molecule.PYFD2 and PYFD3 stand out as the most suitable candidates due to their prominent l max values and lowest transition energies.Therefore, they are predicted to be favorable NLO materials.

Nonlinear optical properties
NLO materials are widely used in the optoelectronic devices, telecommunications, optical interconnections, signal and networking manipulation.The strength of the optical response is related to the electrical properties of material, which are inuenced by both linear and non-linear properties, i.e., hai, b tot and g tot. 53In the case of organic molecules, the establishment of NLO response relies on the asymmetric polarization caused by the push-pull architecture of organic chromophores. 54owever, the strength of asymmetric polarization is inuenced by the chemical nature of various donor and acceptor components, which are connected via the p-spacer in the D-p-A framework.This research is fascinating as it depicts linear relationship among the linear and nonlinear responses, hence estimating the optical engagements in the studied chromophores.Table 6 lists the major DFT calculated values of the dipole moment (m total ), average linear polarizability (hai), and rst (b tot ) and second hyper-polarizabilities (g tot ) of the investigated compounds (PYFR and PYFD1-PYFD7), while Tables S35-S38 † show their contributing tensors.
The electronegativity and polarity of a substance can cause the dipole moments; the larger electronegativity difference marked the higher dipole moments (m). 55Moreover, m total is known as a three-dimensional parameter, which established a relationship between the positive and negative centers of charges in a molecule and their inuence over the intra-molecular charge transfer (ICT). 56The calculated m total of the reference compound (PYFR) is The average linear polarizability (hai) predicts the linear optical activity of a molecule, which determines the rate of the intramolecular charge transfer (ICT). 57Table S36 † shows the detailed results, which include the cartesian coordinates (x, y, z) components, along with the average linear polarizability isotropies for the designed compounds.The conversion factor employed for this purpose is 1 a.u = 1.4819 × 10 −25 esu.The hai values are obtained as 1.072, 1.750, 1.861, 1.899, 1.872, 1.819, 1.834 and 1.752 × 10 −22 esu for the PYFR and PYFD1-PYFD7 compounds, respectively.The impact of end-capped acceptors is predominantly observed in the designed organic chromophores (PYFD1-PYFD7).The highest hai is obtained for PYFD3 as 1.899 × 10 −22 esu.The results also showed that the linear polarizability is dominant along the x-axis, as indicated by the higher values of a xx tensors as compared to a yy and a zz (Table S36 †).This also proved that the maximum intramolecular charge transfer occurs in the x-orientation for the studied molecules.The average polarizability decreases in the following order: PYFD3 > PYFD4 > PYFD2 > PYFD6 > PYFD5 > PYFD7 > PYFD1 > PYFR.This tendency suggests that all developed compounds are more potent than the reference chromophore (PYFR).
Tables S37 and S38 † presented the average values alongside with their respective tensor coordinates in the x, y and z directions.The results showed that the b tot values were enhanced with the presence of electron-withdrawing acceptor substituents in the case of PYFD1-PYFD7, hence contributing to a signicant NLO response.PYFD2 exhibits the most potent electron-withdrawing groups (-NO 2 ) in the 2-( 2 S34 †).The maximum average value of the second hyper-polarizability (g tot ) is observed for PYFD2 (4.631 × 10 −33 esu).Just like hai, the g tot is also composed of three components along the 3-D plane (g x , g y and g z ).The greatest amplitude in this case is shown by the g x tensor (Table S35  Frequency-dependent rst hyperpolarizability (b(u)) coefficients, including the electro-optic Pockel's effect (EOPE) with b(−u; u,0) and the second-harmonic generation of rst hyperpolarizability (SHG) with b(−2u; u,u), 58 is a time-dependent eld.From Table S38, † it can be observed that the rst hyperpolarizability (b(u)) coefficients are dependent on the wavelengths.The EOPE values are largely enhanced as compared to the static rst hyperpolarizability values of the PYFR and PYFD1-PYFD7 chromophores.At 1907.21 nm, the EOPE and SHG values are found in the range of 1.823 × 10 −29 -5.048 × 10 −28 and 2.388 × 10 −29 -6.904 × 10 −28 e.s.u., respectively, whereas the response is reduced to be 1.650 × 10 −29 -4.937 × 10 −28 e.s.u. at static wavelength (0.00 nm).All the designed chromophores have their maximum EOPE and SHG values at 1907.21 nm, indicating the resonant enhancement for EOPE and SHG of the chromophores.Compound PYFD2 shows the best value of EOPE and SHG at 1907.21 nm, which is found to be 5.048 × 10 −28 and 6.904 × 10 −28 e.s.u.Similar to the third order nonlinear optical response coefficients (the dc-Kerr effect g(−u; u,0,0)), the electric eld induced a second harmonic generation (ESHG) g(−2u; u,u,0) 59 due to the application of the timedependent eld.The computed results are listed in Table S40, † where one can be seen that all of the designed derivatives show a large dc-Kerr effect g(−u; u,0,0) and electric eldinduced second harmonic generation (ESHG) g(−2u; u,u,0) values at the specic frequency.The enormously higher dc-Kerr effect and ESHG values are observed for the PYFD2 derivative, which are found to be 4.883 × 10 −33 and 7.539 × 10 −33 , respectively, at 1907.21 nm, indicating that both dc-Kerr effect and ESHG values can be remarkably enhanced at higher wavelength for the designed derivatives.Additionally, a comparative study is made between our designed chromophores with the reported ndings of compounds DFPPC and DCPPC. 60The ndings of the designed chromophores (PYFR and PYFD1-PYFD7) show remarkable results in terms of the linear polarizability and second hyperpolarizability values as compared to the DFPPC and DCPPC compounds.Specically, the linear polarizability values of the designed chromophores (PYFR and PYFD1-PYFD7) were also found to be 4.10, 6.69, 7.12, 7.28, 7.16, 6.97, 7.02 and 6.71 times greater than that for compound DFPPC (2.6116 × 10 −23 esu), respectively, and 3.491, 5.69, 6.06, 6.18, 6.10, 5.92, 5.97 and 5.70 times greater than that for compound DCPPC (3.0772 × 10 −23 esu), respectively.Similarly, the nonlinear second hyperpolarizability values of the designed derivatives (PYFR and PYFD1-PYFD7) were observed to be 33.19 By comparing the b tot values of the designed compound (PYFR and PYFD1-PYFD7) with para-nitroaniline, it is observed that the b tot values of the designed derivatives (PYFD1-PYFD7) were 255, 31.51,76.31, 63.96, 67.51, 53.28, 37.60 and 34.13  times greater than that of para-nitroaniline (b tot = 6.46 × 10 −30 esu), respectively.Moreover, the g tot values of the designed derivatives are 147.5, 400.41, 635.25, 550.07, 585.58, 484, 475.4 and 410 times greater than that of the standard compound (para-nitroaniline, g tot = 7.29 × 10 −36 ), respectively. 61

Conclusion
The current study consists of a series of compounds, namely PYFD1-PYFD7 and reference compound (PYFR).The strategically placed thiophene molecules, by replacing the benzene spacer unit, as well as various acceptors at one end, were substituted in all structures to create a push-pull architecture to achieve a higher non-linear optical (NLO) response.A quantum chemical investigation was conducted to examine the impact of molecular engineering for NLO characteristics.All of the designed chromophores showed a wider absorption range in the visible region, with a decreased range of energy gap (2.340-2.604eV).Consequently, they demonstrated efficient charge transfer from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) as compared to the reference chromophore.The soness decreases in the following order: PYFD2 > PYFD3 > PYFD4 > PYFD5 > PYFD6 > PYFD7 > PYFD1 > PYFR.So, it was observed that all of the molecules exhibited higher polarizability.Overall, the decreasing order of g tot values in esu is shown as follows: PYFD2 > PYFD4 > PYFD3 > PYFD5 > PYFD6 > PYFD7 > PYFD1 > PYFR.It can be concluded from the aforementioned discussion that all chromophores exhibited a much higher nonlinear optical (NLO) response as compared to the reference compound.This computational study offers valuable insights for experimental researchers to investigate the potential of these appealing nonlinear optical (NLO) materials in the elds of nonlinear optics and electronics.
where, b x = b xxx + b xyy + b xzz , b y = b yxx + b yyy + b yzz and b z = b zxx + b zyy + b zzz .The dynamic (frequency dependent) rst hyperpolarizability is denoted by: b

Table 1
Calculated energies: E HOMO , E LUMO , and energy gap (DE) of the designed compounds in eV

Table 2
The calculated GRPs of PYFR and MTRID1-MTRID7 a

Table 3
Nominated values of NBOs analysis for PYFR and PYFD1-PYFD7

Table 4
Calculated binding energy (E b ) of the designed compounds in eV total values in the range of 10.013-17.780D.The increase in m total is signicantly attributed to the modication in the D-p-D conguration of PYFR into the D-p-A conguration in the designed compounds, accompanied by the incorporation of potent electron-withdrawing groups.The highest dipole moments are seen in PYFD3 (17.780D) and PYFD4 (16.438D) due to the presence of strong electron-withdrawing groups such as -SO 3 H and -CN, respectively.The changes in the dipole moments (beside the x, y and z directions) were also studied.Their contributing tensor values are recorded in TableS35, † which shows that the highest contributing tensor is m z , i.e., 5.677 and 5.028 D obtained for PYFD3 and PYFD4, respectively.